Interpolation routines for cubic and higher order interpolation. More...

#include <iostream>
#include <cmath>
#include "interpolation_poly.h"
#include "interpolation.h"
#include "logic.h"
#include "check_input.h"
#include "arts_omp.h"

Include dependency graph for interpolation_poly.cc:

Go to the source code of this file.

Macros
#define	LOOPW(x) for ( ConstIterator1D x = t##x##begin; x!=t##x##end; ++x)
	Macro for interpolation weight loops. More...

#define	CACHEW(x)
	Macro for caching begin and end iterators for interpolation weight loops. More...

#define	LOOPIDX(x) for (ArrayOfIndex::const_iterator x=t##x##begin; x!=t##x##end; ++x)
	Macro for interpolation index loops. More...

#define	CACHEIDX(x)
	Macro for caching begin and end iterators for interpolation index loops. More...

Functions
Index	IMAX (Index a, Index b)
	Return the maximum of two integer numbers. More...

Index	IMIN (Index a, Index b)
	Return the minimum of two integer numbers. More...

void	gridpos_poly (ArrayOfGridPosPoly &gp, ConstVectorView old_grid, ConstVectorView new_grid, const Index order, const Numeric &extpolfac)
	Set up grid positions for higher order interpolation. More...

void	gridpos_poly (GridPosPoly &gp, ConstVectorView old_grid, const Numeric &new_grid, const Index order, const Numeric &extpolfac)
	gridpos_poly More...

void	gridpos_poly_longitudinal (const String &error_msg, ArrayOfGridPosPoly &gp, ConstVectorView old_grid, ConstVectorView new_grid, const Index order, const Numeric &extpolfac)
	Set up grid positions for higher order interpolation on longitudes. More...

void	gridpos_poly_cyclic_longitudinal (ArrayOfGridPosPoly &gp, ConstVectorView old_grid, ConstVectorView new_grid, const Index order, const Numeric &extpolfac)
	Set up grid positions for higher order interpolation. More...

ostream &	operator<< (ostream &os, const GridPosPoly &gp)
	Output operator for GridPosPoly. More...

void	interpweights (VectorView itw, const GridPosPoly &tc)
	Red 1D interpolation weights. More...

void	interpweights (VectorView itw, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 2D interpolation weights. More...

void	interpweights (VectorView itw, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 3D interpolation weights. More...

void	interpweights (VectorView itw, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 4D interpolation weights. More...

void	interpweights (VectorView itw, const GridPosPoly &ts, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 5D interpolation weights. More...

void	interpweights (VectorView itw, const GridPosPoly &tv, const GridPosPoly &ts, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 6D interpolation weights. More...

Numeric	interp (ConstVectorView itw, ConstVectorView a, const GridPosPoly &tc)
	Red 1D Interpolate. More...

Numeric	interp (ConstVectorView itw, ConstMatrixView a, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 2D Interpolate. More...

Numeric	interp (ConstVectorView itw, ConstTensor3View a, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 3D Interpolate. More...

Numeric	interp (ConstVectorView itw, ConstTensor4View a, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 4D Interpolate. More...

Numeric	interp (ConstVectorView itw, ConstTensor5View a, const GridPosPoly &ts, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 5D Interpolate. More...

Numeric	interp (ConstVectorView itw, ConstTensor6View a, const GridPosPoly &tv, const GridPosPoly &ts, const GridPosPoly &tb, const GridPosPoly &tp, const GridPosPoly &tr, const GridPosPoly &tc)
	Red 6D Interpolate. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &cgp)
	Compute 1D interpolation weights. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 2D interpolation weights for a sequence of positions. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 3D interpolation weights for a sequence of positions. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 4D interpolation weights for a sequence of positions. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 5D interpolation weights for a sequence of positions. More...

void	interpweights (MatrixView itw, const ArrayOfGridPosPoly &vgp, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 6D interpolation weights for a sequence of positions. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstVectorView a, const ArrayOfGridPosPoly &cgp)
	Interpolate 1D field. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstMatrixView a, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 2D field to a sequence of positions. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstTensor3View a, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 3D field to a sequence of positions. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstTensor4View a, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 4D field to a sequence of positions. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstTensor5View a, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 5D field to a sequence of positions. More...

void	interp (VectorView ia, ConstMatrixView itw, ConstTensor6View a, const ArrayOfGridPosPoly &vgp, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 6D field to a sequence of positions. More...

void	interpweights (Tensor3View itw, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 2D interpolation weights for an entire field. More...

void	interpweights (Tensor4View itw, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 3D interpolation weights for an entire field. More...

void	interpweights (Tensor5View itw, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 4D interpolation weights for an entire field. More...

void	interpweights (Tensor6View itw, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 5D interpolation weights for an entire field. More...

void	interpweights (Tensor7View itw, const ArrayOfGridPosPoly &vgp, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Compute 6D interpolation weights for an entire field. More...

void	interp (MatrixView ia, ConstTensor3View itw, ConstMatrixView a, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 2D field to another 2D field. More...

void	interp (Tensor3View ia, ConstTensor4View itw, ConstTensor3View a, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 3D field to another 3D field. More...

void	interp (Tensor4View ia, ConstTensor5View itw, ConstTensor4View a, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 4D field to another 4D field. More...

void	interp (Tensor5View ia, ConstTensor6View itw, ConstTensor5View a, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 5D field to another 5D field. More...

void	interp (Tensor6View ia, ConstTensor7View itw, ConstTensor6View a, const ArrayOfGridPosPoly &vgp, const ArrayOfGridPosPoly &sgp, const ArrayOfGridPosPoly &bgp, const ArrayOfGridPosPoly &pgp, const ArrayOfGridPosPoly &rgp, const ArrayOfGridPosPoly &cgp)
	Interpolate 6D field to another 6D field. More...

Variables
const Numeric	sum_check_epsilon = 1e-6
	The maximum difference from 1 that we allow for a sum check. More...

Detailed Description

Interpolation routines for cubic and higher order interpolation.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-02-04

The data structures and functions provided here follow the same philosophy as those for linear interpolation in interpolation{.h,.cc}. You will need a sequence of three steps to perform an interpolation:

gridpos_poly (one for each interpolation dimension)
interpweights
interp

Not only is the philosophy the same, these higher order functions also make direct use of the linear functions in some important cases.

Definition in file interpolation_poly.cc.

Macro Definition Documentation

◆ CACHEIDX

#define CACHEIDX ( x )

Value:

const ArrayOfIndex::const_iterator t##x##begin = t##x.idx.begin(); \

const ArrayOfIndex::const_iterator t##x##end = t##x.idx.end();

Macro for caching begin and end iterators for interpolation index loops.

Definition at line 421 of file interpolation_poly.cc.

Referenced by interp().

◆ CACHEW

#define CACHEW ( x )

Value:

const ConstIterator1D t##x##begin = t##x.w.begin(); \

const ConstIterator1D t##x##end = t##x.w.end();

ConstIterator1D

The constant iterator class for sub vectors.

Definition: matpackI.h:249

Macro for caching begin and end iterators for interpolation weight loops.

Definition at line 409 of file interpolation_poly.cc.

Referenced by interpweights().

◆ LOOPIDX

#define LOOPIDX ( x ) for (ArrayOfIndex::const_iterator x=t##x##begin; x!=t##x##end; ++x)

Macro for interpolation index loops.

This is the same as LOOPW, but for loops over tx.idx. Since tx.idx is an ArrayOfIndex, not a Vector, we have to use a different type of iterator.

Definition at line 418 of file interpolation_poly.cc.

Referenced by interp().

◆ LOOPW

#define LOOPW ( x ) for ( ConstIterator1D x = t##x##begin; x!=t##x##end; ++x)

Macro for interpolation weight loops.

We use the macro LOOPW to make the notation for the nested for loops in the interpweights functions more concise, and to avoid typing errors.

Should resolve to something like:

for ( Index x=0; x<tx.w.nelem(); ++x )

But with iterators:

for ( ConstIterator1D x=tx.w.begin(); x!=tx.w.end(); ++x )

Definition at line 406 of file interpolation_poly.cc.

Referenced by interpweights().

Function Documentation

◆ gridpos_poly() [1/2]

void gridpos_poly	(	ArrayOfGridPosPoly &	gp,
		ConstVectorView	old_grid,
		ConstVectorView	new_grid,
		const Index	order,
		const Numeric &	extpolfac
	)

Set up grid positions for higher order interpolation.

This function performs the same task as gridpos, but for arbitrary orders of interpolation. (Linear is also possible, as a special case.) We even handle nearest neighbour interpolation, as order 0.

The formula for calculating the weights w is taken from Numerical Recipes, 2nd edition, section 3.1, eq. 3.1.1.

Parameters

gp	Output: An array of grid positions.
old_grid	Original grid.
new_grid	New grid.
order	Interpolation order. 0 = nearest neighbour, 1 = linear, 2 = quadratic, etc.. The number of points used in the interpolation will be order+1.
extpolfac	Extrapolation fraction. Should normally not be specified, then the default of 0.5 is used.

Definition at line 127 of file interpolation_poly.cc.

References gridpos(), IMAX(), IMIN(), is_size(), and ConstVectorView::nelem().

Referenced by abs_lookupCalc(), abs_lookupSetupBatch(), abs_lookupTestAccMC(), GasAbsLookup::Adapt(), AtmFieldsCalc(), IsotopologueRecord::CalculatePartitionFctAtTempFromData(), choose_abs_nls_pert(), choose_abs_t_pert(), cia_interpolation(), GasAbsLookup::Extract(), fos(), GriddedFieldLatLonRegridHelper(), GriddedFieldZToPRegridHelper(), gridpos_poly(), gridpos_poly_cyclic_longitudinal(), gridpos_poly_longitudinal(), iyInterpCloudboxField2(), jacobianCalcFreqShift(), jacobianCalcFreqStretch(), p2gridpos_poly(), sensor_responseFillFgrid(), surface_reflectivityFromGriddedField6(), surface_scalar_reflectivityFromGriddedField4(), test07(), and test08().

◆ gridpos_poly() [2/2]

void gridpos_poly	(	GridPosPoly &	gp,
		ConstVectorView	old_grid,
		const Numeric &	new_grid,
		const Index	order,
		const Numeric &	extpolfac
	)

gridpos_poly

Creates a grid position structure for higher order interpolation.

This is a gateway to the function for arrays of GridPosPoly, to be used for e.g. "red interpolation".

Return values

gp	The GridPos structure.

Parameters

old_grid	The original grid.
new_grid	The position where we want to have the interpolated value.
order	Interpolation order. 1 = linear, 2 = quadratic, etc.. The number of points used in the interpolation will be order+1.
extpolfac	Extrapolation factor. Default value is 0.5, which means that extrapolation of half of the last grid distance is allowed. You don't have to specify this.

Author: Stefan Buehler

Date: 2008-03-06

Definition at line 266 of file interpolation_poly.cc.

References gridpos_poly().

◆ gridpos_poly_cyclic_longitudinal()

void gridpos_poly_cyclic_longitudinal	(	ArrayOfGridPosPoly &	gp,
		ConstVectorView	old_grid,
		ConstVectorView	new_grid,
		const Index	order,
		const Numeric &	extpolfac
	)

Set up grid positions for higher order interpolation.

This function performs the same task as gridpos, but for arbitrary orders of interpolation. It is especially for cyclic interpolation of longitudes. The distance between the first and the last point in the original grid has to span 360 degrees.

Parameters

[out]	gp	An array of grid positions.
[in]	old_grid	Original grid.
[in]	new_grid	New grid.
[in]	order	Interpolation order. 1 = linear, 2 = quadratic, etc.. The number of points used in the interpolation will be order+1.
[in]	extpolfac	Extrapolation fraction. Should normally not be specified, then the default of 0.5 is used.

Author: Oliver Lemke

Date: 12-07-10

Definition at line 359 of file interpolation_poly.cc.

References gridpos_poly(), is_lon_cyclic(), and ConstVectorView::nelem().

Referenced by gridpos_poly_longitudinal().

◆ gridpos_poly_longitudinal()

void gridpos_poly_longitudinal	(	const String &	error_msg,
		ArrayOfGridPosPoly &	gp,
		ConstVectorView	old_grid,
		ConstVectorView	new_grid,
		const Index	order,
		const Numeric &	extpolfac
	)

Set up grid positions for higher order interpolation on longitudes.

This function performs the same task as gridpos, but for arbitrary orders of interpolation. It is especially for interpolation of longitudes. If necessary, it will shift the given longitudes up or down by 360 degrees. For a global longitude grid, it will do cyclic interpolation.

The formula for calculating the weights w is taken from Numerical Recipes, 2nd edition, section 3.1, eq. 3.1.1.

Parameters

[in]	error_msg	Message for potential runtime error
[out]	gp	An array of grid positions.
[in]	old_grid	Original grid.
[in]	new_grid	New grid.
[in]	order	Interpolation order. 1 = linear, 2 = quadratic, etc.. The number of points used in the interpolation will be order+1.
[in]	extpolfac	Extrapolation fraction. Should normally not be specified, then the default of 0.5 is used.

Author: Oliver Lemke

Date: 12-07-10

Definition at line 302 of file interpolation_poly.cc.

References chk_interpolation_grids(), gridpos_poly(), gridpos_poly_cyclic_longitudinal(), is_lon_cyclic(), and ConstVectorView::nelem().

Referenced by GriddedFieldLatLonRegridHelper().

◆ IMAX()

Index IMAX	(	Index	a,
		Index	b
	)

Return the maximum of two integer numbers.

This function is based on a macro from Numerical Receipes. The original macro:

static Index imaxarg1, imaxarg2; #define IMAX(a,b) (imaxarg1=(a), imaxarg2=(b),(imaxarg1) > (imaxarg2) ? \ (imaxarg1) : (imaxarg2))

The macro can cause trouble if used in parallel regions, so we use this function instead.

Parameters

a	Input a.
b	Input b.

Returns: The maximum of a and b.

Definition at line 65 of file interpolation_poly.cc.

Referenced by gridpos_poly().

◆ IMIN()

Index IMIN	(	Index	a,
		Index	b
	)

Return the minimum of two integer numbers.

This function is based on a macro from Numerical Receipes. The original macro:

static Index iminarg1, iminarg2; #define IMIN(a,b) (iminarg1=(a), iminarg2=(b),(iminarg1) < (iminarg2) ? \ (iminarg1) : (iminarg2))

The macro can cause trouble if used in parallel regions, so we use this function instead.

Parameters

a	Input a.
b	Input b.

Returns: The minimum of a and b.

Definition at line 87 of file interpolation_poly.cc.

Referenced by gridpos_poly().

◆ interp() [1/17]

Numeric interp	(	ConstVectorView	itw,
		ConstVectorView	a,
		const GridPosPoly &	tc
	)

Red 1D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 730 of file interpolation_poly.cc.

References CACHEIDX, ConstVectorView::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [2/17]

Numeric interp	(	ConstVectorView	itw,
		ConstMatrixView	a,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 2D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 773 of file interpolation_poly.cc.

References CACHEIDX, ConstVectorView::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [3/17]

Numeric interp	(	ConstVectorView	itw,
		ConstTensor3View	a,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 3D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 823 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor3View::get(), ConstVectorView::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [4/17]

Numeric interp	(	ConstVectorView	itw,
		ConstTensor4View	a,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 4D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 879 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor4View::get(), ConstVectorView::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [5/17]

Numeric interp	(	ConstVectorView	itw,
		ConstTensor5View	a,
		const GridPosPoly &	ts,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 5D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
ts	The grid position for the shelf dimension.
tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 941 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor5View::get(), ConstVectorView::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [6/17]

Numeric interp	(	ConstVectorView	itw,
		ConstTensor6View	a,
		const GridPosPoly &	tv,
		const GridPosPoly &	ts,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 6D Interpolate.

"Red" interpolation returns just a scalar.

The dimension of itw must be consistent with the dimension of the interpolation (2^n).

Parameters

itw	Interpolation weights.
a	The field to interpolate.
tv	The grid position for the vitrine dimension.
ts	The grid position for the shelf dimension.
tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Returns: Interpolated value.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1009 of file interpolation_poly.cc.

References CACHEIDX, ConstVectorView::get(), ConstTensor6View::get(), is_same_within_epsilon(), is_size(), LOOPIDX, ConstVectorView::nelem(), ConstVectorView::sum(), sum_check_epsilon, and GridPosPoly::w.

◆ interp() [7/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstVectorView	a,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 1D field.

For this 1D case there is no distinction between "blue" and "green" type interpolation.

The output vector ia must have the same length as the grid position vector cgp. And the dimension of itw must be consistent with this.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1491 of file interpolation_poly.cc.

References CACHEIDX, ConstVectorView::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [8/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstMatrixView	a,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 2D field to a sequence of positions.

This performs a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The output vector ia also must have the same length. And the dimension of itw must be consistent with this.

This function can be easily distinguished from the other interpolation function (that creates an entire field of interpolated values), because of the dimension of ia and itw.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1551 of file interpolation_poly.cc.

References CACHEIDX, ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [9/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstTensor3View	a,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 3D field to a sequence of positions.

This performs a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The output vector ia also must have the same length. And the dimension of itw must be consistent with this.

This function can be easily distinguished from the other interpolation function (that creates an entire field of interpolated values), because of the dimension of ia and itw.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1619 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor3View::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [10/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstTensor4View	a,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 4D field to a sequence of positions.

This performs a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The output vector ia also must have the same length. And the dimension of itw must be consistent with this.

This function can be easily distinguished from the other interpolation function (that creates an entire field of interpolated values), because of the dimension of ia and itw.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1695 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor4View::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [11/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstTensor5View	a,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 5D field to a sequence of positions.

This performs a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The output vector ia also must have the same length. And the dimension of itw must be consistent with this.

This function can be easily distinguished from the other interpolation function (that creates an entire field of interpolated values), because of the dimension of ia and itw.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1779 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor5View::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [12/17]

void interp	(	VectorView	ia,
		ConstMatrixView	itw,
		ConstTensor6View	a,
		const ArrayOfGridPosPoly &	vgp,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 6D field to a sequence of positions.

This performs a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The output vector ia also must have the same length. And the dimension of itw must be consistent with this.

This function can be easily distinguished from the other interpolation function (that creates an entire field of interpolated values), because of the dimension of ia and itw.

Return values

ia	Vector containing the interpolated field values.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
vgp	The grid position Array for the vitrine dimension.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1871 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor6View::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [13/17]

void interp	(	MatrixView	ia,
		ConstTensor3View	itw,
		ConstMatrixView	a,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 2D field to another 2D field.

This performs a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

This function can be easily distinguished from the other interpolation function (that creates a sequence of interpolated values), because of the dimension of ia and itw.

The size of ia and itw in all dimensions must be consistent with the grid position Arrays.

Return values

ia	Interpolated field.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2359 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor3View::get(), ConstMatrixView::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [14/17]

void interp	(	Tensor3View	ia,
		ConstTensor4View	itw,
		ConstTensor3View	a,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 3D field to another 3D field.

This performs a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

This function can be easily distinguished from the other interpolation function (that creates a sequence of interpolated values), because of the dimension of ia and itw.

The size of ia and itw in all dimensions must be consistent with the grid position Arrays.

Return values

ia	Interpolated field.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2432 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor3View::get(), ConstTensor4View::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [15/17]

void interp	(	Tensor4View	ia,
		ConstTensor5View	itw,
		ConstTensor4View	a,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 4D field to another 4D field.

This performs a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

This function can be easily distinguished from the other interpolation function (that creates a sequence of interpolated values), because of the dimension of ia and itw.

The size of ia and itw in all dimensions must be consistent with the grid position Arrays.

Return values

ia	Interpolated field.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2517 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor4View::get(), ConstTensor5View::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), sum_check_epsilon, and w().

◆ interp() [16/17]

void interp	(	Tensor5View	ia,
		ConstTensor6View	itw,
		ConstTensor5View	a,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 5D field to another 5D field.

This performs a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

This function can be easily distinguished from the other interpolation function (that creates a sequence of interpolated values), because of the dimension of ia and itw.

The size of ia and itw in all dimensions must be consistent with the grid position Arrays.

Return values

ia	Interpolated field.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2613 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor5View::get(), ConstTensor6View::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), ns, sum_check_epsilon, and w().

◆ interp() [17/17]

void interp	(	Tensor6View	ia,
		ConstTensor7View	itw,
		ConstTensor6View	a,
		const ArrayOfGridPosPoly &	vgp,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Interpolate 6D field to another 6D field.

This performs a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

This function can be easily distinguished from the other interpolation function (that creates a sequence of interpolated values), because of the dimension of ia and itw.

The size of ia and itw in all dimensions must be consistent with the grid position Arrays.

Return values

ia	Interpolated field.

Parameters

itw	Interpolation weights.
a	The field to interpolate.
vgp	The grid position Array for the vitrine dimension.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2720 of file interpolation_poly.cc.

References CACHEIDX, ConstTensor6View::get(), ConstTensor7View::get(), is_same_within_epsilon(), is_size(), joker, LOOPIDX, Array< base >::nelem(), ns, sum_check_epsilon, and w().

◆ interpweights() [1/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	tc
	)

Red 1D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 470 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [2/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 2D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 505 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [3/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 3D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 540 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [4/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 4D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 581 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [5/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	ts,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 5D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

ts	The grid position for the shelf dimension.
tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 627 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [6/17]

void interpweights	(	VectorView	itw,
		const GridPosPoly &	tv,
		const GridPosPoly &	ts,
		const GridPosPoly &	tb,
		const GridPosPoly &	tp,
		const GridPosPoly &	tr,
		const GridPosPoly &	tc
	)

Red 6D interpolation weights.

"Red" interpolation returns just a scalar, so the weights are stored in a Vector.

The length of itw must be consistent with the dimension of the field to be interpolated (2^n).

Return values

itw	Interpolation weights.

Parameters

tv	The grid position for the vitrine dimension.
ts	The grid position for the shelf dimension.
tb	The grid position for the book dimension.
tp	The grid position for the page dimension.
tr	The grid position for the row dimension.
tc	The grid position for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 678 of file interpolation_poly.cc.

References CACHEW, VectorView::get(), is_size(), LOOPW, ConstVectorView::nelem(), and GridPosPoly::w.

◆ interpweights() [7/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 1D interpolation weights.

For this 1D case there is no distinction between "blue" and "green" type interpolation.

The dimensions of itw must be consistent with cgp.

Note that we still do not need the actual field for this step.

Return values

itw	Interpolation weights.

Parameters

cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1083 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [8/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 2D interpolation weights for a sequence of positions.

Compute the weights for a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The dimensions of itw must be also consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Matrix, whereas in the other case it is a Tensor with one more dimension than there are input grid position Arrays.

Return values

itw	Interpolation weights.

Parameters

rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1158 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [9/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 3D interpolation weights for a sequence of positions.

Compute the weights for a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The dimensions of itw must be also consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Matrix, whereas in the other case it is a Tensor with one more dimension than there are input grid position Arrays.

Return values

itw	Interpolation weights.

Parameters

pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1219 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [10/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 4D interpolation weights for a sequence of positions.

Compute the weights for a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The dimensions of itw must be also consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Matrix, whereas in the other case it is a Tensor with one more dimension than there are input grid position Arrays.

Return values

itw	Interpolation weights.

Parameters

bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1279 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [11/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 5D interpolation weights for a sequence of positions.

Compute the weights for a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The dimensions of itw must be also consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Matrix, whereas in the other case it is a Tensor with one more dimension than there are input grid position Arrays.

Return values

itw	Interpolation weights.

Parameters

sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1346 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [12/17]

void interpweights	(	MatrixView	itw,
		const ArrayOfGridPosPoly &	vgp,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 6D interpolation weights for a sequence of positions.

Compute the weights for a "blue" type interpolation of the field, that means that the grid position Arrays are interpreted as defining a sequence of positions. ALL GRID POSITION ARRAYS MUST HAVE THE SAME LENGTH!

The dimensions of itw must be also consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Matrix, whereas in the other case it is a Tensor with one more dimension than there are input grid position Arrays.

Return values

itw	Interpolation weights.

Parameters

vgp	The grid position Array for the vitrine dimension.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1420 of file interpolation_poly.cc.

References CACHEW, MatrixView::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [13/17]

void interpweights	(	Tensor3View	itw,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 2D interpolation weights for an entire field.

Compute the weights for a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

The dimensions of itw must be consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Tensor with one more dimension than the number of grid position Arrays.

Return values

itw	Interpolation weights

Parameters

rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 1970 of file interpolation_poly.cc.

References CACHEW, Tensor3View::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [14/17]

void interpweights	(	Tensor4View	itw,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 3D interpolation weights for an entire field.

Compute the weights for a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

The dimensions of itw must be consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Tensor with one more dimension than the number of grid position Arrays.

Return values

itw	Interpolation weights

Parameters

pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2036 of file interpolation_poly.cc.

References CACHEW, Tensor4View::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [15/17]

void interpweights	(	Tensor5View	itw,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 4D interpolation weights for an entire field.

Compute the weights for a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

The dimensions of itw must be consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Tensor with one more dimension than the number of grid position Arrays.

Return values

itw	Interpolation weights

Parameters

bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2103 of file interpolation_poly.cc.

References CACHEW, Tensor5View::get(), is_size(), LOOPW, Array< base >::nelem(), and w().

◆ interpweights() [16/17]

void interpweights	(	Tensor6View	itw,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 5D interpolation weights for an entire field.

Compute the weights for a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

The dimensions of itw must be consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Tensor with one more dimension than the number of grid position Arrays.

Return values

itw	Interpolation weights

Parameters

sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2180 of file interpolation_poly.cc.

References CACHEW, Tensor6View::get(), is_size(), LOOPW, Array< base >::nelem(), ns, and w().

◆ interpweights() [17/17]

void interpweights	(	Tensor7View	itw,
		const ArrayOfGridPosPoly &	vgp,
		const ArrayOfGridPosPoly &	sgp,
		const ArrayOfGridPosPoly &	bgp,
		const ArrayOfGridPosPoly &	pgp,
		const ArrayOfGridPosPoly &	rgp,
		const ArrayOfGridPosPoly &	cgp
	)

Compute 6D interpolation weights for an entire field.

Compute the weights for a "green" type interpolation of the field, that means that the grid position Arrays are interpreted as defining the grids for the interpolated field.

The dimensions of itw must be consistent with this.

Note that we still do not need the actual field for this step.

This function can be easily distinguished from the other interpweights function (for "green" interpolation), because the output is a Tensor with one more dimension than the number of grid position Arrays.

Return values

itw	Interpolation weights

Parameters

vgp	The grid position Array for the vitrine dimension.
sgp	The grid position Array for the shelf dimension.
bgp	The grid position Array for the book dimension.
pgp	The grid position Array for the page dimension.
rgp	The grid position Array for the row dimension.
cgp	The grid position Array for the column dimension.

Author: Stefan Buehler <sbuehler(at)ltu.se>

Date: 2008-03-06

Definition at line 2267 of file interpolation_poly.cc.

References CACHEW, Tensor7View::get(), is_size(), LOOPW, Array< base >::nelem(), ns, and w().

◆ operator<<()

ostream& operator<<	(	ostream &	os,
		const GridPosPoly &	gp
	)

Output operator for GridPosPoly.

This is just intended for testing and debugging.

Parameters

os	Output stream.
gp	Grid position.

Returns: The output stream.

Definition at line 434 of file interpolation_poly.cc.

References GridPosPoly::idx, and GridPosPoly::w.

Variable Documentation

◆ sum_check_epsilon

const Numeric sum_check_epsilon = 1e-6

The maximum difference from 1 that we allow for a sum check.

The sum check makes sure that the sum of all weights is approximately 1.

We cannot use a sharp comparison there, due to numerical noise. The value of 1e-6 is an ad-hoc value.

This shold be ok, the main point of the test is to make sure that what we have really are interpolation weights, and not something else.

Definition at line 106 of file interpolation_poly.cc.

Referenced by interp().

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

◆ CACHEIDX

◆ CACHEW

◆ LOOPIDX

◆ LOOPW

Function Documentation

◆ gridpos_poly() [1/2]

◆ gridpos_poly() [2/2]

◆ gridpos_poly_cyclic_longitudinal()

◆ gridpos_poly_longitudinal()

◆ IMAX()

◆ IMIN()

◆ interp() [1/17]

◆ interp() [2/17]

◆ interp() [3/17]

◆ interp() [4/17]

◆ interp() [5/17]

◆ interp() [6/17]

◆ interp() [7/17]

◆ interp() [8/17]

◆ interp() [9/17]

◆ interp() [10/17]

◆ interp() [11/17]

◆ interp() [12/17]

◆ interp() [13/17]

◆ interp() [14/17]

◆ interp() [15/17]

◆ interp() [16/17]

◆ interp() [17/17]

◆ interpweights() [1/17]

◆ interpweights() [2/17]

◆ interpweights() [3/17]

◆ interpweights() [4/17]

◆ interpweights() [5/17]

◆ interpweights() [6/17]

◆ interpweights() [7/17]

◆ interpweights() [8/17]

◆ interpweights() [9/17]

◆ interpweights() [10/17]

◆ interpweights() [11/17]

◆ interpweights() [12/17]

◆ interpweights() [13/17]

◆ interpweights() [14/17]

◆ interpweights() [15/17]

◆ interpweights() [16/17]

◆ interpweights() [17/17]

◆ operator<<()

Variable Documentation

◆ sum_check_epsilon